"The Israeli army's leadership allowed the reopening of stores on Sahla Street, which runs from the area near the Ibrahimi mosque" through Hebron's old town, Dawud al-Zaatari told journalists.
"This is the first time the army has allowed these shops to open since the beginning of the second intifada" or uprising in 2000, he added.
After hearing the news, three owners immediately dashed to their stores to unlock the doors and peer inside, an AFP photographer said, but they were forbidden by soldiers from opening yet.
"We were informed they'll be allowed to reopen on Friday," Zaatari said, without elaborating.
Signup to our newsletter and follow us on Facebook and Twitter!
The Israeli army would also be easing movement restrictions ahead of the Muslim holy month of Ramadan, Zaatari said, by opening two roads south of the occupied city which have been closed for years.
The military could not immediately confirm or deny the Palestinian mayor's statements.
The army closed more than 500 Hebron shops during the second intifada, most of them along the deserted Shuhada (martyrs) Street near the old town, according to a local planning official.
Hebron, the scene of regular hostilities between Arabs and Jews, is home to nearly 200,000 Palestinians.
There are also some 80 settler homes in the centre of town housing around 700 Jews who live under Israeli army protection.